Minimal Symmetric PAKE and 1-out-of-N OT from Programmable-Once Public Functions
Ian McQuoid, Mike Rosulek, Lawrence Roy · 2020
Symmetric password-authenticated key exchange (sPAKE) can be seen as an extension of traditional key exchange where two parties agree on a shared key if and only if they share a common secret (possibly low-entropy) password. We present the first sPAKE protocol to simultaneously achieve the following properties: only two exponentiations per party, the same as plain unauthenticated Diffie-Hellman key agreement (and likely optimal); optimal round complexity: a single flow (one message from each party that can be sent in parallel) to achieve implicit authentication, or two flows to achieve explicit mutual authentication; security in the random oracle model, rather than ideal cipher or generic group model; UC security, rather than game-based. Our protocol is a generalization of the seminal EKE protocol of Bellovin & Merritt (S&P 1992).